A geometry problem by Krishna Shankar

Note $-1\le\sin x\le 1\forall x\in\mathfrak R$ . Also since $a^x$ is an increasing function for real $'a'$ , we can write $a^x\in [a^{-1},a^{1}]$ . Hence $2^x+3^x+6^x\in\color{#D61F06}{[}2^{-1}+3^{-1}+6^{-1},2+3+6]=\color{#D61F06}{[}1,11]$ . Hence according to the question we have the case when minimum value of expression occurs ie when $\sin x=-1$ and least integer satisfying this criteria is $x=270^{\circ}$ .